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Like somebody else said, the evidence you have is immensely misinterpreting the semantics. Jigen by itself is merely "root" or "origin," it only becomes "dimension," if you combine the two letters together. Cho, on the other hand, simply, as said, means "beyond." So, if we take this into account, this doesn't mean "beyond the order of dimensionality," it simply means "beyond dimensions." And that brings me to my next point, jigen doesn't mean "dimensionality," nor was it ever shown to mean dimensionality as a whole, it simply translates to "dimensions."
And the cherry on top to all of this is that this doesn't even equate to higher-dimensionality without further context. "Dimensions" here have to be proven to be actual spatial dimensions, and "transcend" has to refer to actual qualitive superiority and not just something that could define position. So, without any further context, all this could be is a different dimension, which is actually a conclusion that is congenial to make since the writers themself took this into account.
And the cherry on top to all of this is that this doesn't even equate to higher-dimensionality without further context. "Dimensions" here have to be proven to be actual spatial dimensions, and "transcend" has to refer to actual qualitive superiority and not just something that could define position. So, without any further context, all this could be is a different dimension, which is actually a conclusion that is congenial to make since the writers themself took this into account.